You can unlock additional heroes by obtaining the hero cards. You can find these cards in daily, golden, or epic chests. Because these are the legendary cards, they are very rare to drop. You can check the drop chance right in the store by tapping on each chest. This is what the hero card looks like:
The first legendary (hero) card you find unlocks the hero for you to use and upgrade to up to level 33. The next card of the same hero lets you upgrade them up to level 66 and the 3rd card of the same hero lets you upgrade it up to level 99.
Hero cards cannot drop from the Unkilled chest. Instead, this chest has a chance to drop exclusive hero skins instead. You can find more info about the Unkilled chest here.